On non-repetitive sequences of arithmetic progressions:the cases k∈{4,5,6,7,8}

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43957769" target="_blank" >RIV/49777513:23520/20:43957769 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2019.10.013" target="_blank" >https://doi.org/10.1016/j.dam.2019.10.013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2019.10.013" target="_blank" >10.1016/j.dam.2019.10.013</a>

Result language
angličtina
Original language name
On non-repetitive sequences of arithmetic progressions:the cases k∈{4,5,6,7,8}
Original language description
A k-Thue sequence is a sequence in which every d-subsequence, for 1⩽d⩽k, is non-repetitive, i.e. it contains no consecutive equal subsequences. In 2002, Grytczuk proposed a conjecture that for any k, k+2 symbols are enough to construct a k-Thue sequence of arbitrary lengths. So far, the conjecture has been confirmed for k∈{1,2,3,5}. Here, we present two different proving techniques, and confirm it for all k, with 2⩽k⩽8.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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